EP2948985A1

EP2948985A1 - Three-dimensional metamaterial device with photovoltaic bristles

Info

Publication number: EP2948985A1
Application number: EP14743882.4A
Authority: EP
Inventors: Mark Schroeder; Robert Smith
Original assignee: Q1 Nanosystems Corp
Current assignee: Q1 Nanosystems Corp
Priority date: 2013-01-28
Filing date: 2014-01-28
Publication date: 2015-12-02
Also published as: EP2948985A4; WO2014117183A1; US9082911B2; US9076908B2; CN105144406A; HK1214409A1; US20140209155A1; KR20150112012A; US20140209160A1

Abstract

The systems, methods, and devices of the various embodiments provide a photovoltaic cell made up of an array of photovoltaic bristles. The photovoltaic bristles may be configured individually and in an array to have a high probability of photon absorption. The high probability of photon absorption may result in high light energy conversion efficiency.

Description

TITLE

l¾ree~Dimensional Metamaterial Device with Photovoltaic Bristles RELATED APPLICATION

[0001 This application claims priority to ^'U.S. Application No. 13/751 , 14, filed January 28, 2013, and to U.S. Application No. 13/763.073, filed February 8, 2013. The entire contents of Applications 13/751 , 14 and 13/763,073 are incorporated by reference herein.

FIELD

[0002] This application generally relates to photovoltaic devices, and more specifically to photovoltaic cells featuring a large number of photovoltaic bristles.

BACKGROUND

[0003] Solar energy is a popular clean energy, but it is generally more expensive than its carbon based competitors (e.g., oil, coal, and natural gas) and other traditional non- carbon based energy sources (e.g., hydropower). Typically, solar energy is also relatively expensive because traditional photovoltaic cells with a planar configuration have generally low total efficiency. Total efficiency is based upon the total power produced from a solar cell throughout the day as the sun transits across the sky. Total efficiency is different from the theoretical efficiency of converting to eiectricity a given amount of light energy striking the photovoltaic cells with a zero angle of incidence (e.g., the instant when the sun is directly above the solar cell).

SUMMARY

10004 ] The systems, methods, and de v ices of the various embodiments provide a photovoltaic cell featuring a metamaterial formed from a plurality of photovoltaic bristles whose photovoltaic and conductive materials are configured to exhibit a high probability of photon absorption and internal reflection. As a res ult of the high probability of photon absorption and internal photon reflections, the nietarnaterial of photovoltaic bristles exhibits high total efficiency in convening light energy into electrical energy. The high total efficiency of the embodiment photovoltaic cells may lead to increased efficiency and more power generation from the photovoltaic cell.

[0005) The various embodiments also include structural features that may result in reduced resistance to electrical current when exposed to light sufficient to generate electrical potentials. Such enhanced conductivity may further efficiency and net power generated from the photovoltaic cell under certain operating conditions.

BRIEF DESCRIPTION OF THE DRAWINGS

[0006] The accompanying drawings, which are incorporated herein and constitute part of this specification, illustrate exemplary embodiments of the invention, and together with the general description given above and the detailed description given below, serve to explain the features of the invention.

[0007] FIG. I A is a perspective view of a number of photovoltaic bristles extending from a substrate to form a metamaterial according to an embodiment.

[0008] FIG, IB is a top view of the photovoltaic bristles illustrated in FIG, I A.

[0009] FIG. 1C is a cross-sectional view of a conventional photovoltaic device illustrating a wave front of photons.

[0010] FIG. 1 D is a perspective view of photovoltaic bristles illustrating photon interactions when an axis of the array of photovoliaic bristles is oriented at an angle to the incident photons.

[0011] FIG . 2 A is a cross-sectional top view of a section of an embodiment in which the photovoltaic bristles have a conductive core and two absorber sublayers or regions. [0012] FIG. 2B is a cross-sectional side view of the photovoltaic bristles illustrated in FIG. 2A.

[0013] FIG. 2C is a cross-sectional top view of one of the photovoltaic bristles illustrated in FIG. 2A.

[0014] FIG, 2D is a cross-sectional side view of one of the photovoltaic bristles illustrated in FIG. 2A.

[0015 ] FIG. 2E is a di agram illustrati ng off angle elements of a photon wave interacting with a circular cross-section photovoltaic bristle.

[00161 FIG. 3 A is a cross-sectional top view of a section of an embodiment in which photovoltaic bristles have a conductive core and three absorber sublayers or regions.

[0017] FIG , 3B is a cross-sectional side view of the photovoltaic bristles illustrated in FIG. 3A.

[0018] FIG. 3C is a cross-sectional top view of one of the photovoltaic bristles illustrated in FIG. 3A.

[0019] FIG. 3D is a cross-sectional side view of one photovoltaic bristle of the photovoltaic cell illustrated in FIG. 3 A.

[0020] FIG. 4 A is a cross-sectional top view of a section of an embodiment in which photovoltaic bristles have a layered conductive core and two absorber sublayers or regions.

[0021] FIG, 4B is a cross-sectional side v view of the photovoltaic bristles illustrated in FIG. 4A.

[0022] FI G . 4C is a cross-sectional top view of one of the photovoltaic bristles iilustraied in FIG. 4 A. [0023] FIG. 4D is a cross-sectional side view of one of the photovoltaic bristles illustrated in FIG. 4.A..

[0024] FIG. 5 A is a cross-sectional top view of a section of an embodiment in which photovoltaic bristles have a layered conductive core and three absorber sublayers or regions.

[0025] FIG. 5B is a cross-sectional side view of the photovoltaic brisiies il lustrated in FIG. 5A.

[0026] FIG. 5C is a cross-sectional top view of one of the photovoltaic bristles illustrated in FIG. 5A,

[0027] FIG, 5D is a cross-sec tional side view of one of the photovoltaic bristles illustrated in FIG. 5 A.

[0028] FIG. 6A is a cross-sectional top view of a section of an embodiment in which photovoltaic bristles have a semiconductor core and one absorber sublayer.

[0029] FIG. 6B is a cross-sectional side view of the photovoltaic bristles illustrated in FIG. 6A.

[0030] FIG . 6C i a cross-sectional top view of one of the photo voltaic bristles illustrated in FIG, 6A.

[0031 ] FIG. 61) is a cross-sectional side view of one of the photovoltaic bristles illustrated in FIG. 6 A.

[0032] FIG, 7 A is a cross-sectional top view of a section of an embodiment in which photovoltaic bristles have a doped semiconductor core and two absorber sublayers or regions. |O 33| FIG. 7B is a cross-sectional side view of the photovoltaic bristles illustrated in FIG. 7A.

[0034] FIG. 7C is a cross-sectional top vie w of one of the photovoltaic bristles illustrated in FIG. 7A.

[003S] FIG, 7D is a cross-sectional side view of one of the photovoltaic bristles illustrated in FIG. 7A.

[0036] FIG. S illustrates an embodiment method for manufacturing photovoltaic cells according to the various embodiments.

[0037] FIG. 9 i a cross-sectional side view of an array of photovol taic bristles illustrating charge concentrations at structural discontinuities, which may occur when the array is exposed to light.

[0038] FIGs. I OA- 10D illustrates embodiments of the outer conductive layer including multiple sublayers.

[0039] FIG. 1 1 is a cross-sectional view of an arra of photovoltaic bristles

superimposed with an electro-magnetic Held strength graphic illustrating the results of an electro-dynamics analysis of photon interactions with the photovoltaic bristle's absorption layer using.

DETAILED DESCRIPTION

[0040] The various embodiments will be described in detail with reference to the accompanying drawings. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts. The terms "example,"

"exemplar^' " or any term of the like are used herein to mean serving as an example, instance, or illustration. References made to particular examples and implementations are for illustrati ve purposes, and are not intended to limit the scope of the invention or the claims. Any implementation described herein as an "example" is not necessarily to be construed as preferred or advantageous over another implementation.

[0041] As used herein, the term "photovoltaic bristle" refers to a three-dimensional structure approximately cylindrical with a height approximately equal to I - 100 microns, a diameter of approximately 0.2 - 50 microns that includes at least one photovoltaieally- active semiconductor layer sandwiched between a conductive inner layer or core and a transparent outer conductive layer. The term "bristle" is used merely because the structures have a length greater than their diameter, the structures have a generally (on average) circular cross-section, and the overal l dimensions of the structures are on the dimensions of sub-microns to tens of microns, in the embodiment illustrated herein the photovoltaic bristles have an approximately cylindrical, by which it is meant that a substantial portion of the exterior surface of the structures have a cross-section that is approximatel circular or elliptical with both radii being approximately coexistent. Due to manufacturing variability, no single photovoltaic bristle may be exactly cylindrical in profile, but when considered ove a large number of photovoltaic bristles the average profile is cylindrical. In another embodiment, the photovoltaic bristles may have a non- circular cross-section, such as hexagonal, octagonal, elliptical, etc. as may facilitate manufacturing.

[0042) When the embodiment photovoltaic bristles are arranged on a substrate in an order or disordered array, the resulting structure may form a metamaterial structure. As used herein, the term "metamaterial" or "metamaterial substrate" refers to an array of photovoltaic bristles on a substrate. Metaniaterial s as used herein are artificial materials thai are engineered with metals or polymers that are arranged in a particular structured or non-structured pattern that result in material properties (including light absorption and refraction properties) that are different, from the component materials. The cumulative effect of light interacting with the array of photovoltaic bristles may be affected by controlling the shape, geometry, size, orientation, material properties, material thicknesses, and arrangement, of the bristles making up the metamaterial as described herein.

[0043] Traditional planar photovoltaic cells are flat. In traditional planar photovoltaic cells, a limited number of photons are absorbed at any given point in time. Photon absorption occurs through the thickness of the traditional planar photovoltaic cell (e.g., top-to-bottom) from the point of photon entry until the photon is converted to electrical energy. Traditional planar photovoltaic cells convert photons into electrical energy when photons interact with a photovoltaic layer. However, some photons pass through the photovoltaic layer without generating electron-hole pairs, and thus represent lost energy. While the number of photons absorbed may be increased by making the photovoltaic- layer thicker, increasing the thickness i ncreases the fraction of electron-hole pairs that recombine, converting their electrical potential into heat. Additionally, thicker photovoltaic films exhibit an exponential attenuation loss leading to a decrease in photon conversion. For this reason, traditional planar photovoltaic cells have emphasized thin photovoltaic layers, accepting the reduced photon-absorption rate in favor of increased conversion of electron-hole pairs into electrical current and reduced heating. The theoretical peak efficiency, a well as the total efficiency, of traditional planar

photovoltaic cells is thus limited by the planar geometry and the im-attenuated fraction of photons that can be absorbed in a maximized optical path length through the photovoltaic layer.

[004 1 Conventional planar photovoltaic cells also suffer from low total efficiency in static deployments (i.e., without su tracking equipment), since their instantaneous power conversion efficiency decreases significantly when the sun is not directly overhead (i.e., before and after noon). Peak efficiencies of traditional planar photovoltaic cells are affected by their orientation with respect to the sun, which may change depending on the time of day and the season. The standard test conditions for calculating peak efficiencies of solar cells are based on optimum conditions, such as testing the photovoltaic cells at solar noon or with a light source directly above the cells. If light strikes traditional photovoltaic cells at an acute angle to the surface (i.e., other than perpendicular to the surface) the instantaneous power conversion efficiency is much less than the peak efficiency. Traditional planar photovoltaic cells in the northern hemisphere are typically tilted toward the south by an angle based on the latitude in order to improve their efficiency. While such fixed angles may account for the angle of the sun at noon due to latitude, the photovoltaic cells receive sun light at an angle dining the morning and afternoon i.e., most of the day). Thus, traditional planar photovoltaic cells actuall result in a low total efficiency and low total power generation when measured beyond a single moment in time.

[0045] The various embodiments include photovoltaic cells that exhibit metamaierial characteristics from regular or irregular arrays of photovoltaic bristles configured so the conversion of light, into electricity occurs within layers of the photovoltaic bristles. Since the photovoltaic bristles extend above the surface of the substrate and are spaced apart, the arrays pro vide the photovoltaic ceils of the various embodiments with volumetric photon absorption properties that lead to energ conversion performance that exceeds the levels achievable with traditional planar photovoltaic cells. The volumetric photon absorption properties eoable the various embodiment photovoltaic cells to generate more power than traditional planar photovoltaic cells with the same footprint Due to the small size of the photovoltaic bristles, the phoiovoltaicaily-active layers within each bristle are relatively thin, minimizing power losses doe to electron-hole recombination. The thin photovoltaieally-aetive layers help reduce attenuation losses normally present in thicker photovoltaic films because the photovoltaic bristles include a thin radial absorption depth and a relatively thicker vertical absorption depth maximizing photon absorption and power generation. ^'When individual photovoltaic bristles are combined in an array on, or within, a substrate, a metamaterial structure may be formed that exhibits a high probability of photon absorption and internal reflection that leads to increased energy conversion efficiencies and power generation. Various embodiment structures also provide additional performance-enhancing benefits as will be described in more detail below.

[0046] The various embodiments include configurations for positioning photovoltaic bristles on a substrate with inter-bristle spaeings dependent on the dimensions of each bristle that trade-off shadowing and photon absorption opportunities in order to increase the energy conversion performance. These embodiment configurations may be determined based upon specific dimensions, enabling a range of photovoltaic cell con figurations depending upon the height and diameter of the photovoltaic bristles. Due to the small size of the photovoltaic bristles and the relatively short distance between bristles, the result may be a metamaterial in which light waves (i.e., photons when evaluated as waves instead of particles) exhibit a higher probabi lity of interacting with and being absorbed by the materials of the photovoltaic bristles than occurs with conventional photovoltaic cells. Additionally the three-dimensional structure of the photovoltaic bristles increases the optical thickness of the metamaterial device. Ail of these factors increase the numbe of photons that are absorbed into the photovoltaically- active layers of the photovoltaic bristles, and thus increase the amount of light energy that is available for conversion to electricity.

[0047 j The various embodiments also include configurations of the conductive and photovoltaically-aetive layers within each photovoltaic bristle in terms of thickness and index of refraction that provide enhanced power conversion performance by internally refracting photons absorbed within the bristles. As described in more detail below, photons may essentially reflect and propagate around the photovoltaic bristle's absorption annulus thereby developing an equilibrium standing wave. Photons that makeup the standing wave will be absorbed and converted into an electron hole pair. This circular internally reflecting photon path and the resulting standing wave are unique to the various embodiments, and a phenomenon that cannot occur in a conventional planar photovoltaic [0048] Further performance enhancements may be obtained by positioning the embodime t photovoltaic cells so that the photovoltaic bristles are at an angle to the incident photons. This can improve the probability that photons will be absorbed into the photovoltaic bristles due to wave interactions between photons and the outer conductive layer on each photovoltaic bristle. Orienting the embodiment photovoltaic cells at an angle to the incident photons also increases the optical depth of the photovoltaic bristles exposed to the light, since in such an orientat ion the photons strike the sides of the bristles and not just the tops. The off-axis photon absorbing characteristics of the photovoltaic bristles also enables the embodiment photovoltaic cells to exhibit significant total energy conversion efficiency for indirect and scattered light, thereby increasing the number of photons of available for absorption compared to a conventi onal photovoltaic cell,

[0049] In a further effect resulting from the bristle-type structure of the various embodiments, increased amounts of current obtained from an embodiment photovoltaic cell has been found to result from decreases in the resistance of the transparent conductive layers during insolation. This may be caused in pari by electric field concentrations that can develop at points of structural discontinuity within the arrays of photovoltaic bristles, which may lead to increased conductivity due to field effects similar to what happens in field effect transistors. Analysis and observations of prototypes indicates that this reduction in resistance i ncreases as die thickness of the outer conductive layer increases, This decrease in resistance with decrease i outer conductive layer thicknes runs counter to conventional wisdom, which holds the opposite effect. Conventional photovoltaic cells utilize relatively thick conductive oxide layers in order to reduce power losses due to excessive resistance in that layer. In the embodiment, thicker outer conductive layers are undesirable because they increase the minimum diameter of the bristles and reduce the packing density within the photovoltaic cell. Larger diameter photovoltaic bristles may exhibit lower photon absorption characteristics and reduce the photon absorbing characteristics of the metamaterial formed from arrays of such bristles. Thus, the observed reductions in resistance i photovoltaic bristles with thin outer conductive layers enables the design of more efficient embodiment photovoltaic cells by enabling the use of thin outer conducti ve layers, which may enable smaller diameter bristles and higher packing densities, ail without increasing electrical losses due to increases in resistance of the thinner outer conductive layer.

[005 J The compound effect of all of these energy con version performance

improvements is high total energy efficiency and high total power generation. The total energy efficiency includes a higher peak performance at optimum conditions, hut more importantly, it includes a higher sustained average efficiency over an entire day. This means that the embodiment solar cells may generate more power during a day by producing more power than conventional photovoltaic cells before and after solar noon. Tims, with production costs expected to be only slightly more expensive than

conventional photovoltaic cells (which ha ve benefited from decades of production refinements), the significant improvement in overall energy conversion performance of the various embodiments is expected to result in photovoltaic arrays that can be cost competitive with conventional electrical power generation technologies, such as coal and natural gas power plants.

10051] FIG, 1 A illustrates an embodiment photovoltaic cell 100 made up of an array of photovoltaic bristles 101a, 101b, 101c, fOld, 101 e, l OI f, !Olg, lOlh, lOli, IQlj, 101k, 1011, 10 Im, 101 n, 101 o, I01p extending from a substrate 102. While illustrated w ith twelve photovoltaic bristles l Ola-IOl p in FIG. 1 A, a photovoltaic cell 1.00 may include a large number of photovoltaic bristles, which forms a metamaterial structure. The number of photovoltaic bristles 101 on any photovoltaic cell 100 wi ll depend upo the

dimensions and spacing of the bristles and the size of the cell. As with conventional photovoltaic cells, individual photovoltaic ceils 100 may be assembled together in large numbers to form panels (i.e., solar panels) of a size that are suitable for a variety of installations, 10052] Each photovoltaic bristle 101 a- 10 p is characterized by its height "A," which is the distance that each bristle extends from the substrate 102. Photovoltaic bristles 10 ! a- l Olp are also characterized by their radius 'V\ In an embodiment, ail photovoltaic bristles lOl a-lOlp within an array will have approximately the same height h and approximately the same radius r in order to facilitate manufacturing. However, i other embodiments, photovoltaic bristles lOla-lOlp within the array may be manufactured with different height and diameters.

§0053] in an embodiment, the number of photovoltaic bristles in a photovoltaic cell may depend upon the substrate surface area available within the cell and the packing density or inter-bristle spacing. As explained in more detail below, in an embodiment, photovoltaic bristles may be positioned on the substrate with a packing density or inter- bristle spacing that is determined based upon the bristle dimensions (i.e., h and r dimensions) as well as other parameters, and/or pattern variations. For example, a hexagonal pattern rather than the trigonometric pattern described, also metaniaterial patterns of variations within the ordered arrays,

[0054] In the various embodiments, the dimensions and the inter-bristle spacing of photovoltaic bristles may be balanced against the shading of neighboring bristles. In other words, increasing the number of pbotovoltaic bristles may increase the surface area available for absorbing photons. However, each photovoltaic bristle casts a small shadow, so increasing the photovoltaic bristle density of a photovoltaic cell beyond a certain point may result In a significant portion of each bristle being shadowed by its neighbors. While such shadowing may not reduce the number of photons thai are absorbed within the array, shadowing may decrease the number of photons that are absorbed by each photovoltaic bristle, and thus there may be a plateau in the photon absorption versus packing density of photovoltaic bristles. A further consideration beyond shadowing is the wave interaction effects of the array of closely packed photovoltaic bristles. The interior-bristle spacing may be adjusted to increase the probability that photons entering the array are absorbed by the photovoltaic bristles" meianiaierial properties considering the bulk material properties of the layered fi lms that makeup the array. For example, specific characteristics such as extinction coefficient or absorption path length may predict an optimal dimensional design, although one may chose to deviate from this prediction resulting its a sacrifice in performance.

(0055] FIG. IB shows a top view of the photovoltaic ceil 100 illustrating the inter- bristle dimensions in an arbitrary arrangement of bristles. As will he further described below, the arrangement of bristles is show as having a diamond or trapezoidal pattern, may also be any other ordered pattern (e.g., hexagonal pattern, octagonal pattem) or non- order pattern such as a swirl. As mentioned above, each photovoltaic bristle 101 a- 10 S p is characterized by a radius r that is measured from the center to the outer surface of the photovoltaic bristle 101 a- 101 p. in an embodiment, the radius r of each photovoltaic bristl 101a~101p may be the same. In another embodiment, the radius r of the photovoltaic bristles may be different or vary.

(0056] In an embodiment, the array of photovoltaic bristles 101 a- 101 p may be formed as rows A, B, C, D that are spaced apart on the substrate 102. While FIG. I B illustrates just four rows of four photovoltaic bristles each, embodiment photovoltaic cells 100 will typically include large numbers of rows with each row including a large number of photovoltaic bristles, forming a metamaierial device.

[0057] The metamaterial configuration of the array of photovoltaic bristles, including the packing density of the photovoltaic bristles, may be defined in terras of inter-bristle dimensions. Th distanc between two neighboring photovoltaic bristles of the array of photovoltaic bristles 101 a- 101 p may be described by their center-to-center spacing or edge-to-edge spacing, in a regular array, the distance between photovoltaic bristles may vary in different directions, so these distances may he referred to as the long pitch and the short pitch. The long pitch may be characterized in terms of the maximum center- to- center spacing, or Long Pitch (LP) or the maximum edge-to-edge spacing. Long Pitch edge-to-edge (LP_f:,_ioe)- The short pitch may be characterized in terms of the minimum eenter-to-center distance or Short Pitch (SP) or minimum edge-to-edge spacing. Short Pitch edge-to-edge (SP_f¾>t-)- The center-to-eenter spacing of the photovoltaic bristles! 01 may be m between SP and LP. in an embodiment, the array of photovoltaic bristles lOla-10 lp may be formed such that the edge-to-edge spacing of all respective

neighboring photovoltaic bristles of the array of photovoltaic bristles 101 a- 101 p may be greater than or equal to SPE_IOE and less than or equal to LP_£M;, The relationship between inter-bristle spacing, radii and height will be explained below beginning with reference to FIG, 2 A.

[0058) A s mentioned above, the height of the photovoltaic bristles above the substrate results in a raeiamaterial 3-D structure that exhibits greater electrical power generation for a given amount of insolation then can be expected from a conventional fiat

photovoltaic cell, of the same area. Part of this effect is due to the depth of the structure over which photons interact with photovoltaicaily-active materials. This effect is illustrated in FlGs, 1 C and 1 D. f 0059] As illustrated in FIG. 1C, a conventional photovoltaic cell 1 10 is generall planar with a photovoltaic active layer 1 1 i applied to a planar substrate 1 12. Due to this planar architecture, incident light rays 120 strike a flat surface. Consequently, photon waves 122 are accurately represented in terms of a flux, which is a measure of the number of photons striking an area (i.e. flat surface) per unit time. Thus, energy conversion performance of conventional photovoltaic cells is measured against the incident photon energy measured as a flux, which is a two-dimensional measurement. Thus, the energy con version efficiency of a conventional photovoltaic cell 110 is based upon the amount of electricity generated by unit area of the cell divided by the photon flux.

[00601 This measurement of the amount of Sight energy interacting with photovoltaic cells is not necessarily appropriate for embodiment photovoltaic cells 1.00 since it ignores the three-dimensional aspect resul ting from the height dimensio of photovol taic bristles. This is illustrated in FIG. I D. which shows incident light rays 120 striking the various surfaces presented to the light b the photovoltaic bristles 101 . Specifically, incident photons 120 may interact with the surface of photovoltaic bristles 101 along their entire length. Thus, incident photons interact with the embodiment photovoltaic ceils 100 throughout the depth of the array defined by the height of the photovoltaic bristles 101. Consequently, at any given instant, the number of photons interacting with the

embodiment photovoltaic cells 100 is equal to the number of photons within the volume defined by a unit area times the heiglrt of the photovoltaic bristles 101 less the subtended angle reduction. The shadow-^' from an eclipsing neighboring photovoltaic bristle reduces the number of photons interacting within the metamaterial and may vary depending on the tilt of the metamaterial. Even with the subtended angle reduction, this volumetric effect means that there are more photons available for interacting with the photovoltaic bristles 10 ! in embodiment photovoltaic cells 1.00 than is possible with conventional planar photovoltaic ceils 1 10.

[0061] Further details of the structures making up photovoltaic bristles are illustrated in FlGs. 2A and 2B, which are cross-sectional views of a photovoltaic ceil 200 made up of an array of photovoltaic bristles 201a, 20 lb, 201 c, and 201 d. formed on a substrate 21.2. In general, photovoltaic bristles are generally cylindrical structures with generally cylindrical layers 203, 204 formed about a central core 206, with photo voliakaliy-aetive material layers 207 sandwiched between conducting materials at or on the core 206 and on the surface, which is a transparent conducting oxide layer 203. When, photons interact with the photovoitaieally-aetive layers 207 electron-hole pairs are generated, which are conducted out of the photovoltaic bristles by the conductive layers 206, 207 to conductive layers on the substrate 212,

[0062] The core 206 may be characterized by a core radius (r_c) that may be measured radially from the cente of the photovoltaic bristle 201 b to the inner surface of the absorption, layer. The core 206 may be made of a variety of conductive materials and non-conducti ve materia ls. In an embodiment, the core 206 of a photovoltaic bristle may be a solid conductive core such as metal. For example, the core of the photovoltaic bristle ma be gold, copper, nickel, molybdenum, iron, aluminum, doped silicon, and silver. In other embodiments, the core of a photovoltaic bristle may made from a non- conductive center, such as a semiconductor or polymer plastic, thai is coated or covered with a conductive layer, such as gold, copper, nickel, molybdenum, iron, aluminum, doped silicon, or silver. In an embodiment, the core 206 may also include a coating to strengthen the microstmcture 20 b. In a further embodiment, the core of the photovoltaic bristles may the made from a doped semiconductor material, such as p-type amorphous silicon or n-type amorphous silicon. In another embodiment, the core 206 may be made from a different material than the substrate 212. In an embodiment, the core 206 may be made from the same material as the substrate 212.

10063 ] The photovoltaic bristle includes an absorption layer 207 made up of one or more sublayers 204, 205 of photovoltaieally-active materials that are configured to generate electron-hole pairs when a photon is absorbed. In an embodiment, the absorption layer 207 may include a p-type semiconductor sublayer (204 or 205} and an n~ type semiconductor sublayer (205 or 204} forming a p-n junction within the absorptioii layer 207. For example, the p-type and the n-type semiconductor sublayers may be appropriately doped amorphous silicon, in anotlier embodiment, the absorption layer 207 may include a p-type semiconductor sublayer, an intrinsic semiconductor sublayer, and an n-type semiconductor sublayer. For example, the p-type semiconductor, the intrinsic semiconductor, and the n-type semiconductor sublayers may be amorphous silicon. In a further embodiment, the absorption layer 207 of a photovoltaic bristle may be a single doped semiconductor sublayer forming a p-n junction with the core 206 that is doped to be either a p- or n-semieonductor. For example, in this embodiment the core 206 may be a p-type semiconductor and the absorption layer 207 may an n-type semiconductor layer.

[0064] As mentioned above, embodiment photovoltaic cells may be configured with bristle-packing densities defined according to the materials and dimensions of the photovoltaic bristles. As mentioned above, photovoltaic bristles 201 a- 2 Id have a radius r measured from the center of the photovoltaic bristle to the outer perimeter of the photovoltaic bristle. For purposes of calculating the bristle packing density; the mean radius r_m of the bristles may be used since the individual radii may vary due to the variability of manufacturing techniques.

[0065] Each photovoltaic bristle 20Ia-201d is made up of a core 206 that is conductive or has a conductive outer surface, absorption layer 207, and an outer conductive layer 203, which will typically be transparent conductive layer such as a transparent conductive oxide or transparent conductive nitride. Doe to the cylindrical form of photo voltaic bristles, the absorption layer 207 surrounds the core 206, and the outer conductive layer 203 surrounds the absorption layer 207, The absorption layer 207 as radial thickness (d_3¾>s) that may be meas ured radial ly from the outer surface of the core 206 to the inner surface of the outer conductive layer 203. The absorption layer 207 may include a number of absorber sublayers or regions of pliotovoliaically-active materials or combinations of photovoltaic materials. For example, the absorption layer 207 may include multiple absorber sublayers or regions that form a p-n junction, a p~i-n junction, or multi-j nction regions, which have a generally circular cross-section as illustrated in FIG. 2A. The absorber sublayers or regions 204, 302, 205 may be made from one or more of silicon, amorphous silicon, polycrystalHne silicon, single crystal silicon, cadmium telluride, gallium arsenide, aluminum gallium arsenide, cadmium sulfide, copper indium se.leni.de, and copper indium gallium, selenide,

[0066] The relative radial positions of the p-type, intrinsic, or n-type sublayers/regions may vary in the embodiments. For example, in. one embodiment the p-type

semiconductor material may be positioned radially inside the n-type semiconductor material, in another embodiment, the n-type semiconductor material may be positioned radially inside the p-type semiconductor material, in addition, multiple materials may be used to create a sequence of p-n and/or n-p junction s, or p-i-n junctions in the absorption layer. For example, the absorption layer may include an absorber sublayer of p-type cadmium telluride (CdTe) and an absorber sublayer of n-type cadmium sulfide (CdS). In an embodiment, the absorption layer 20? may be fully depleted. For example, tbe p-type region and the n-type region forming the sublayer or region 204 and tbe sublayer or region 205 may be fully depleted.

[0067] In an example embodiment, the absorption layer 207 may include a p-type semiconductor sublaye 205, such as p-type cadmium telluride, and an n-type

semiconductor sublayer of a different material , such as n-type-cadmium sulfide. In another example embodiment, one sublayer 204 may be a p-type region, such as p-type amorphous silicon, and another sublayer 205 may be an n-type region of the same material as the sublayer 204 but doped to form an n-type semiconductor, such as n-type amorphous silicon.

[00681 For purposes of illustration, the absorption layer 207 radial thi ckness (d^) may encompass ail the absorber sublayers or regions. In various embodiments, the absorption layer 207 thickness (d«bs) may be less than 0. 1 microns, approximately 0.01 microns, or greater than 0.01 microns. Embodiment absorber thickness (d_;,!_)¾) ranges include 0.01 to 0.10 microns, 0.10 to 0.20 microns, 0.20 to 0.30 microns, 030 to 0.40 microns, 0.40 to 0.50 microns, 0.50 to 0,60 microns, 0.60 to 0.70 microns, 0.70 to 0.80 microns, 0.80 to 0.90 microns, 0.90 to 1.0 microns, 0. 1 to 1.0 microns, and more than 1.0 microns. In an example embodiment, the absorption layer 207 thickness (d_ab_$) may be approximately 0.64 microns subject to variability in the manufacturing process by which the absorption layers are applied to the core 206.

[0069] The outer conductive layer 203 has a radial thickness (d_<ic¾) which may be measured radially from the outer surface of the absorption layer 207 to the outer suriace of the outer conductive layer 203 (i.e., the outer surface of the photovoltaic bristle). In an embodiment, the outer conducti ve layer 203 is a transparent conductive oxide CTCO"), such as a metal oxide, in an embodiment, the outer conductive layer 203 may include a dopant creating a p-type or n-type transparent conductive oxide. For example, the transparent conductive oxide layer 203 may be one of intrinsic zinc oxide, indium tm oxide, and cadmium tin oxide (Cd^SnO^). in an embodiment, the outer conductive layer 203 may include a transparent conductive nitride such as titanium, nitride (TiN). In another embodiment, the outer conductive layer 203 may include a buffer with or without the dopant. Some examples of an outer conductive layer 203, which may be a transparent conductive oxide with a dopant, include boron doped zinc oxide, fluorine doped zinc oxide, gallium doped zinc oxide, and aluminum doped zinc oxide. Some examples of buffers that may be added to a transparent conductive oxide include zinc s annate

(Zt SnO,}), titanium dioxide (TiO?), and similar materials well known in the art.

[0070) As shown and described later with FlGs. 1 OA- HID, the outer conductive layer 203 may include a number of multiple conductive and or non-conductive sublayers to allow a photovoltaic bristle to meet the required design optical thickness ) while simultaneously benefiting from the field effects generated from a thin transparent conductive sublayer within the outer conductive layer 203. With multiple sublayers, the outer conductive laye 203 ma also benefit from added flexibility to the photovoltaic bristles for a more resilient metamateriai device. As an example, a bi-layer outer conductive laye 203 ma include a conductive sublayer such ICQ and a non-conductive sublayer such as an optically transparent polymer.

[0071 j As shown in FIG. 2.B, the photovoltaic bristles extend from a substrate 212 of the photovoltaic cell 200. The substrate 212 may be any suitable substrate material known in the art. For example, the substrate 212 may be glass, doped semiconductor, diamond, metal, a polymer, ceramics, or a variety of composite materials. The material used in the substrate 212 may be a material used elsewhere in the photovoltaic cell 200, such as a material used in any layer of a photovoltaic bristle 201a~201 d. Alternatively, the material used in the substrate 2 12 may be different from the materials in the photovoltaic bristles 201 a~20I . in an embodiment, the core 206 and the substrate 212 may be made from the same base material that is covered by a conductive material. For example, the substrate 212 and the cores 206 ma be made from glass, semiconductor material, a polymer, ceramics, or composites. In a flirther embodiment, the core 206 and substrate 2 1.2 may Include similar materials, while the core 206 is made from additional materials, such as gold, copper, nickel, molybdenum, iron, aluminum, or silver.

[0072] in the various embodiments, the inde of refraction of the outer conductive layer 203 and absorption layer 207 and sublayers 204, 205 as well as the thicknesses of these layers may be configured to increase the probability of absorption of incident photons and internal refraction of absorbed photons as illustrated in FlGs. 2C and 2D. As illustrated in FIG. 2C, photovoltaic bristles 201 designed and formed in accordance with the embodiment designs described below, ma guide an absorbed photon 210 so that it follows an internal path 21 1 that exhibits a high probability that the photon remains within the photovoltaic bristle 201 due to total internal reflection. As illustrated, by adjusting the index of refraction and thickness of each layer 203, 204, 205, a photon may be caused to retract inwardly until it contacts the conductive core 206 where it may be spectrally reflected, it should be noted that the embodiment illustrated in FiGs. 2A-D features and inne reflector due to the metal core 206. in other embodiments described herein, a refraction layer may be applied over the core 206 to achieve the same photon reflection effects, in such an embodiment, a reflective layer may be formed over the conductive core and under the absorber layer, such as a semiconductor or dielectric material layer having a. lower inde of refraction than the absorber layer, This refraction layer may be configured to reflect the photon at the interface between the reflection layer and the absorber layer, and not rel on reflection off of the conductive core 206. For example, such a diffraction layer may be formed from an aluminum doped zinc oxide layer of about 500-1500 angstroms in thickness. Reflected photons then refract through each layer 204, 205 until they reach the outer conductive layer 203, where the difference in the index of retraction between the absorption sublayer 205 and the outer conductive layer 203 causes the photons to reflect back into the absorption layers of the photovoltaic bristle. Those reflected photons that are not reflected inwardly at the boundary between the outer conductive laye 203 and the absorption sublayer 205 may pass through the outer conductive layer 203 and be reflected off of the interface between the outer conductive layer 203 and air due to the difference in the index of refraction at this interface, in either mariner, photons may remain within the photovoltaic bristle passing back and forth through the absorption layer 207 until they are eveiitiially absorbed or exit the bristle.

[0073] FIG. 2D illustrates the photon traveling within and around the photovoltaic bristle 201. Since the photovoltaic bristle 201 extends a distance h above the substrate, a photon 210 entering the bristle at an angle may travel along the axial length or height of the photovoltaic bristle 201 .

[0074] FIG. 2D also illustrates that photons striking the photovoltaic bristle 201 will have a higher probability of absorption when they strike the sidewall of a photovoltaic bristle at a compound angle that is less than 90 degrees but more the 0 degrees to the surface, where an angle perpendicular to the sidewall surface is considered to be 0 degrees. The compound incident angle includes a vertical plane component 233 (shown in FIG. 2D) and a horizontal plane component 232 (shown in FIG, 2C). The horizontal plane component 232 is defined by a photon 210 striking the outer surface of the bristle at a point along the perimeter of the circular cross-section plane forming an angle with the perimete where an angle perpendicular to the perimeter is considered 0 degrees.

Similarly, the vertical plane component 233 is defined by the photon 210 striking the outer surface of the bristle at a point along the height forming a vertical angle with the surface where an angle perpendicular to the surface is considered 0 degrees. Analysis of photon absorption characteristics of the outer conductive layer revealed that photons striking the surface of the sidewall of the photovol taic bristle at: normal in the horizontal componen 232 and the vertical component 233 may result in a compound angle of 0 degrees and a high probability of being reflected off the surface. Similarly, photons striking the surface of the sidewall of the photovoltaic bristle parallel to the vertical and the horizontal component will also have a high probability of being reflected off the surface. However, photons striking the side surface at a compound angle between 10° and 80° have a high probabilit of being absorbed into the outer conductive layer 203, Once absorbed, the internal refraction characteristics of the absorption layers 204, 205 and outer conductive layer 203 cause the photons to remain within the photovoltaic bristle 201 for an extended time or path length. This characteristic is very different from conventional photovoltaic cells, which exhibit the maximum power conversion efficiency when the angle of incidence of photons is normal to its single planar surface.

10075) The difference between the incident angle corresponding to conventional photovoltaic cells and the photovoltaic bristles is illustrated by angle 8_P in FIG. 2D. The preferred incident angle for a traditional solar cell Θ,,, would form a right angle with the top of the bri stle as well as the substrate of the full metarnaterial device (not shown). Thus, not. only does the photovoltaic bristle exhibit better absorption characteristics at off-angles (not perpendicular or parallel to the surface), the reference point for measuring an off-angle is vastly different from a conventional photovoltaic cell. For a metarnaterial device with photovoltaic bristles, the reference point is measured from the side wall of a bristle in two planes, which is unachievable by a planar photovoltaic cell. Thus, due to the off-angle absorption characteristics of photovoltaic bristles, the embodiment photovoltaic cells exhibit significant power conversion efficiency across a broad range of angle of incidence. This translates to more power generation throughout the day than achievable from fixed solar panels with conventional planar solar arrays that produce their peak efficiencies (i.e., emxiroura power generation) when the sun is directly overhead.

[0076] Although conventional planar solar arrays may have high peak efficiency, as described above, peak efficiencies are onl a single point in time. Typically conventional planar photovoltaic cells show a significant drop in efficiency and. power generation in the morning and the afternoon (i.e., not solar noon). Due to the drop in efficiency, the conventional photovoltaic cells have a low total efficiency (or average efficiency) whe measured over an entire day leading to a low total power generation. However, the embodiment .metarnat.eri.als with photovoltaic bristles have sustained high efficiency throughout the day because the compound angle of incidence for the metarnaterial more

^■ 7 closely mirrors that of sun 's presentation of photons. Thus, photons are more likely to strike the sidewails of the photovoltaic bristles 201 with a compoond angle of incidence between approximately 10 and SO degrees resulting in sustained high absorption efficiency and a high total power generation.

(0077] While photovoltaic bristles absorb photons more readily when they strike the surface at an angle, the probability of photon absorption is not a strong function of angle of incidence. This is due to the small diameter and circular cross-section, of photovoltaic bristles and the wave nature of photons. As illustrated in FIG. 2.E, even a photon 210 striking the surface of a photovoltaic bristle 201 at a right angle 220 to the surface will interact with the surface at smaller angles of incidence due to the wave nature of the photon. As illustrated, a photon 2 10 has a wave function that extends beyond its line of travel 21 1 such that there is a probability of the photon interacting with the surface of the photovoltaic bristle 201 some distance from the intersection of the line of travel. Due to the small diameter and circular nature of the bristle, there is a finite probability that the photon will interact with the surface at a smaller angle 222 on either side of the line of travel 21 1. It is also a finite probability that the photon will interact with the surface at even smaller angles 224, 226 a further distance from the line of travel 21 1 . Thus, even a photon that might be expected to be reflected, from a photovoltaic bristle has a significant probability of being absorbed due to the interaction of the photon wave with the curved surface of the bristle.

[0078] As described above, the materials and thicknesses forming the outer conductive layer and absorption layers of the photovoltaic bristle may be selected to resul t in a high probability of photon internal refraction to increase the probability of photon absorption. This may include selecting materials so that the index of refraction of outer transparent conducting oxide layer (r i:) is lower than the index of ref action of the inner absorption layers. For, example the index of refraction of the outer conductive layer may be lower than the index of refraction of the absorption layer. In addition, the index of refraction of outer transparent conducting oxide layer (n {} will be greater than the index of refraction of air (a,., }. Thus, the materials of materials and thicknesses forming the outer conductive layer and absorption layers may be selected so that each layer .moving inward has a higher index of retraction than the preceding outer layer and all layers may have greater indexes of refraction than air.

(0079] By radially ordering the materials by indexes of refractions from a low index of refraction on the outside to a higher index of refraction in each i nner lay er, the

photo voltaic bristle 201 may refract or guide photons 210 towards the core 206 of the photovoltaic bristle 201 . Since the core 206 is highly conductive, it is also highly reflective, so that it will reflect photons 2 1.0. Due to the large difference in index of refraction between the absorber layer and the outer conductive layer 203, photons striking this boundary at an angle will be refracted inwardly. As a result of these reflections and refractions, photons 210 may be effectively trapped within the absorption layer 207 for a longer period of time, thereby increasing the probabi lity of interaction with the absorption layer 207 causing an electron-hole pair to be formed. Increasing the probability of photon absorption may result in more electrical current being generated for the same amount of incident light energy by the embodiment photovoltaic cells than is achievable by conventional photovoltaic cells.

[0080] in an embodiment mentioned above, an inner refraction or reflection layer may be added on top of the core 206 in order to provide an inne reflection interface for photons, in this embodiment, a layer of semi-conductive or insulator material, such as Al:ZnO, ZnO, or ITO, may be applied over the metal core. This layer may be at least one-half wavelength in thickness, depending on the refractive index of the material. For example, such a layer made of AhZnO (AZO) may be approximately 1500 angstroms thick over which the absorber layer may be applied. Such an AZO layer has a refractive index that is lower than the absorber layer. This difference in refractive index coupled with the curvature of the interface of these two layers wiil reflect the photons before they reach the metal core. The reflection induced by this design may exhibit lower losses than then designs in which photons reflect from a metal surface of the core . This additional refraction layer over h core may be included in the equations for determining the photovoltaic bristle diameter as a contributor to the r_t value. In other words, including a 1500 angstrom AZO layer over a .75 micron radius core would result in a core diameter r, for purposes of the design equations of .9 microns. The use of such a refraction layer may be included in any of the embodiments illustrated and described herein. For example, in the embodiments in which the center of the core is a plastic rod, a metal layer is applied over the plastic core and then the AZO is applied over the metal layer. In further embodiments, this refractive layer forming a reflecting interface may be formed using multiple layers, such as: 1TO - AZO; !ΓΟ~ΑΖΟ~ΠΌ; Τϊ0₂-ΊΪΝ-Τί0₂; ZnO-AZO ZnO; etc Such multiple layer may function similar to a Bragg reflector used in fi ber

[0081] The higher energy conversion efficiency enabled by photovoltaic bristles of the various embodiments may be achieved by designing the bristles with outer conductive layer and absorption layer materials and thicknesses, with the bristles spaced apart at a packing density that optimize or nearly optimize the performance enhancement characteristics described above. This may be achieved by designing the photovoltaic bristles and arranging the arrays of the bristles using the following design techniques.

[0082 [ in an embodiment, the outer conductive layer and absorption layer materials and thicknesses of photovoltaic bristles may be selected in set according to equation 1 :

where: r is the bristle core radius;

n_im- is the index of refraction for air;

n_ocl is the index of refraction of the outer conductive layer;

doci is the thickness of the outer conductive layer; and

dabs is the thickness of the absorption layer.

7 [0083] The median radius of a photovoltaic bristle (¾_>) is set according to equation 2: r_m— r_c 4- dab Ί" d-oci 2 where: r_m is the median radi us of the photovoltaic bristles. Thus, the median radius of a photovoltaic bristle (r_M) is the sum of the bristle's core radios (r_c)and the thicknesses of the absoiption layer (d_a},,)and outer conductive layer ( ^ -

[0084] Combining equation 1 and equation 2 and solving for the median radius of the photovoltaic bristles (r_Hi) yields equation 3:

[OOSS] Thus, the radius (r_m) of the photovoltaic bristles may depend upon the First radial thickness (d s), the second radial thickness (d^), the index of refraction of the outer conductive layer (n a d the index of refraction of a ir (i¾,j_r). In other words, a photovoltaic bristle with a ratio as defined in equation 3 will exhibit a high probability of photo internal refraction, and thus exhibit a higher probability of photon absorption and electron-hole generation

[0086) Equation 3 ma also be used to calculate the appropriate thicknesses for the outer conductive layer and absorption layer, since these two layer thicknesses are related in the equation, in order to increase the amount of photovoltaic material, the absoiption layer thickness (d_abS) ma be set to be greater than the outer conducting layer radial thickness {d_()d). However, the outer conductive layer will need to have a minimum thickness in order to maintain desirable conductivity. Thus, there will be a design balance between the two layer thicknesses, in an embodiment, the transparent conducting oxide layer thickness (doci) ma be about two thirds (i.e., approximately sixty- seven percent) of the absorption layer thickness (d_ab$). Thus, in this embodiment, the outer conductive layer thickness ^may be determined by equation 4: d₀a™ 0.67 * d_(tl,s 4

For example, with an absorption layer thickness of approximately 0,64 microns, the outer conductive layer thickness, d_()Cj_? would be approximately 0.43 microns. Although the outer conductive layer may be determined by equation 4, the actual thickness of the outer conductive layer may deviate from this relationship. The actual thickness of the outer conductive layer may be thicker, but thicker outer conductive layers may result in a higher probability that photons will graze off the outer conductive layer instead entering the absorption layer. Thus, equation.4 is merely an exemplary relationship between the thicknesses of outer conductive layer and the absorption layer,

[0087] it is worth noting that the radius of the bristle r_m as defined by equation 2 is important for considerations of inter-bristle spacing in order to address shading issues since thicker bristles cast wider shadows. The core radius r is also a key consideration, particularly for manufacturabtlity and for structural rigidity considerations. While tall thin bristles may be desirable for energy conversion efficiency reasons, there is likely to be a minimum core radius below which photovoltaic bristles cannot be affordably manufactured. Thus, the bristle core radius r_c parameter may be determined based upon the type of manufacturing process used to create them. The bristle core radius r_c parameter may also be determined based upon the strength properties of the material used to form the cores. Stronger materials may enable the bristles to be made smaller in diameter (i.e., with a smaller core radius r_t). On the other hand, weaker materials that may enable lower cost or higher product rates may require the bristles to be made larger in diameter (i.e., with a larger core radius r_c).

[0088] As mentioned above, a photovoltaic cel l 200 including an array of photovoltaic bristles may be designed to achieve high power generation efficiency by reducing the shading of neighboring bristles in the array. The shading caused bv neighboring bristles may be reduced by controlling the minimum edge-to-edge spacing SPB«E) and maximum edge-to-edge spacing photovoltaic bristles. In an embodiment, the minimum edge-to-edge spacing (Sp _ofc) may be calculated using equation 5:

SPstos = * < ) + r_c) * (2) * (0.9) Eq. 5 where (r_c) is the core radi os (e.g., radius of core 206 of photovoltaic bristle 201b as illustrated in FIG. 2 A), and (d_;is,_s} is the thickness of the absorption layer (e.g., thickness of the absorption layer 207). For example, for a bristle having an absorption layer thickness (dabs) of 0.64 microns and a cor radius (r_c) of 0,75 microns, the minimum edge-to-edge spacing CSP&og) would be approximately 3,27 microns. In this

embodiment, the array of photovoltaic bristles may be formed so thai no two neighboring bristles in the array are closer than approximately 3,27 microns.

[0089] The maximum edge-to-edge spacing (LP^E) between photovoltaic bristles may be calculated using equation 6:

= ((1.67 * d_abs) + r_c) * (2) * (1.1) Eq. 6

For example, for photovoltaic bristles having an absorption layer thickness of 0.64 microns and a core radius (r_c) of 0.75 microns, the maximum edge-to-edge spacing

(ΙΛ¾_οΚ) would be approximately 4.0 microns. In this embodiment, the array of

photovoltaic bristles may be formed so that no two neighboring bristles in the array are separated by more than 4,0 microns. Althoug the maximum spacing is given by the example equation 6, bristles may have a larger edge-to-edge spacing than the limits of the equation. However, increasing the edge-to-edge spacing beyond the maximum provided in equation 6 may result in less power generation, due to the lower number of bristles in the metamaterial device. [β090| Equations 4 and 5 may be combined to define the overall edge spacing of neighboring photovoltaic bristles to define the range of edge-to-edge spacing (¾_ΟΕ) -for neighboring photovoltaic bristles as shown in equation 7:

((1.67 * d_abs) + r_c) * (2) * (0.9) < P_moB≤ ((1,67 * d_ab$) + r_c) * (2) * (1.1) Eq, 7

[00911 As an example, photovoltaic bristles with an absorption layer thickness d_abs) f 0,35 microns and a core radius (r_c) of 0.6 microns would be arranged with a minimum edge-to-edge spacing (SP _OE) of approximately 2.13 microns and a maximum edge-to- edge spacing (L ^E) of approximately 2.61 microns. Designing photovoltaic bristles according to equation 1 and designing the array spacing of photovoltaic bristles according to equation 7 may result in a metarnaterial device according to the various embodiments that exhibits significantly higher energy conversion efficiencies than is achievable with conventional photovoltaic panel s.

10092) It is worth noting that the arrays of bristles within the metarnaterial may be ordered or non-ordered. An ordered arra of bristles may have a defined geometric pattern as limited by the trigonometric values such as the short edge-to-edge and long edge-to-edge spacing provided in equation 7. However, the ordered arrays may include a hexagonal pattern instead of a stric t trigonometric pattern meaning that the maximum edge-to-edge spacing of a nei ghboring bristle neighbor spacing may be greater than that listed in equation 6. The ordered array of bristles may also include a diamond pattero, a rectangular pattern, a pentagon, octagon or any other geometric pattern. In an

embodiment, the arrays of bristles may be a non-ordered pattern . The non-ordered pattern of bristles ma be created similar to the ordered-pattern, such as a trigonometric pattern as described in the equations above, but also including a break in the pattern. For example, the bristles may have a standard trigonometric pattern, but every fifth bristle in a row is removed. Alternatively, the metarnaterial may include any non-standard geometric pattern for the bristle arrangement such as a swirling arrangement of bristles. 10093] The height of each photovoltaic bristle within the army of photovoltaic bristles may also affect the probability of photon absorption. In an embodiment, the height of a photovoltaic bristles may be greater than 0.1. microns and less than or equal to 100 microns, to an embodiment, the height of a photovoltaic bristle may be selected based on other characteristics of the array of photovoltaic bristles, including the core radius of each photovoltaic bristle and the spacing between photovoltaic bristles. In pari this selection of the bristle height is made based on the bristle diameter and separation distances to ensure that at. least a portion of the brist le sidewall is not shadowed by adjacent bristles. T his design consideration i a matter of simple geometry onc the bristle core radius and separation distances are selected. As described above, the bristle radius and spacing distances may be determined based upon material indices of refraction and. thicknesses of the absorption layer and transparent conducting oxide layer, and the bristle core radius, each of which may be defined or selected based on the properties of the materials used for these parts of the photovoltaic bristle. Thus, bristle height may also be detennined based on those properties and thicknesses, in short, the entire size and spacing of the photovoltaic bristles in an embodiment photovoltaic cell may be determined by the material properties of the bristle core, absorption layers and transparent conducting oxide.

[0094] The energy conversion efficiency embodiment photovoitaic cells made up of an aoay of photovoltaic bristles may be inereased by designing the photovoltaic bristles with a minimum height (h,_:)::.) that is determined based on the bristle radius and separation distances using equation 7:

where r_c is the radius of the core, and d_abs is the thickness of the absorption layer. For example, with a core radius (r_c) of 0.75 microns and an absorption layer thickness (d_¾te) of 0.64 microns, and the minimum height for the microstructure may be 3.90 microns. In Eq. 7 the term tan (40°) is provided as a design guideline for most applications. However, ibis factor may be replaced with the tangent of any angle up to approximately 80 degrees. The result of increasing the angle would be tal ler bristles. The angle selected in this equation may be adjusted for integrated power gain optimization. This angle may also change depending cm whether the photovoltaic cell will be used for tracking or non- tracking designs.

[0095) With the se ven design formulas described above, a range of embodiment photovoltaic cell designs can be developed that exhibit the desirable energy conversion efficiency characteristics described above. For example, FlGs. 2A-2D illustrate an embodiment in which the absorption layer 207 is made up of to sublayers 204, 205, such as a p-type semiconductor layer and an n-type semiconductor layer to produce a. PN junction absorption layer 207. The embodiment illustrated in FlGs. 2A-2D features a solid conductive core 206, such as a core made from a metal, metal alloy or conductive semiconductor as listed above. However, photovoltaic bristles may also be made with more sublayers, as well as non-conductive cores provided a conductive coating is applied to the core before photovoltaic materia! layers are applied. Oilier example embodiments of photovoltaic cell designs are described below with reference to FlGs 3A-3D, 4A-4D, 5A-5D, 6A-6D, and 7A-7D.

[0096 ] FlGs. 3 A, 3B, 3C, and 3D illustrate an embodiment photovoltaic cell 300 in which the absorption layer 207 in the photo voltaic bristles 201a-201 d include three absorber sublayers or regions 204, 302, 205. In an embodiment, the absorption layer thickness (or a first radial thickness) (c s) is equal to the thicknesses of the three absorber sublayers or regions 204, 302, 205 combined, in an embodiment, the absorber sublayers 204, 302, 205 may be a n~type semiconductor material, an intrinsic semiconductor material, and a p-type semiconductor material, respectively. In an alternative

embodiment, the absorber sublayers may be arranged in the reverse order, such that absorber sublayers 204, 302, 205 may be a p-type semiconductor material, an intrinsic semiconductor material, and a n-type semiconductor material. In another embodiment, the absorber sublayers 204, 302, 205 may be a p-type semiconductor, an tv-type semiconductor, and a p-type semiconductor, respectively. In an embodiment the absorber sublayers 204, 302, 205 may be a n-type semiconductor, a p-type

semiconductor, and a n-type semiconductor, respectively. In an embodiment, the absorption layer may include multiple p-n or p-i-n junctions.

(0097] In various embodiments, the absorber sublayers or regions 204, 302, 205 may made from one or more of silicon, amorphous silicon, polycrystalline si licon, single crystal silicon, cadmium telluride, gallium arsenide, cadmium sulfide, copper indium seienide, and copper indium gallium seienide. In an embodiment, the semiconductor materials for each absorber sublayer 204, 302, 205 may be different semiconductor materials, hi an embodiment, the semiconductor maierials for each absorber sublayer 204, 302, 205 may be the same semiconductor material. For example, absorber regions 204, 302, 205 may include a n-type amorphous silicon, an intrinsic amorphous silicon, and a p-type amorphous silicon.

[0098] In an embodiment, the maierials of the various layers may be selected so that the index of refraction of the outer conductive layer (n_f)C}) is greater than the index of refraction of ai {n_SiK- ), the index of refraction of the outer conductive layer (n^) is less than the index of refraction of the first absorber sublayer 204, the index of refraction of the first absorber sublayer 204 is less than the index of refraction of the third absorber sublayer 302, and the index of refraction of the thi rd absorber sublayer 302 is less than t e index of refraction of the second absorber sublayer 205. In an alternate embodiment, the materials of the various layers may be selected so that the inde of refraction of the outer conducti ve layer (i j) is less than the index of refraction of the absorption layer 207 which i s made up of the three absorber regions 204, 302, 205. As described above, by selecting the layer materials so that there indices of refractions very from a low index of refraction on the outside to a higher index of refraction in each layer moving radially inward, the photovoltaic bristle 201b may refract or guide photons 210 toward the core 206 of the photovoltaic bristle 20 lb as il lustrated in FlGs. 3C and 3D. 10099] FIGs. 4.A, 4B, 4C, and 40 illustrate an embodiment photovoltaic ceil 400 featuring photovoltaic bristles with to sublayers 204, 205 within the absorption layer 207 (similar to the embodiment described above with reference to FIGs. 2A-2D), in which the cores of the photovoltaic bristles ma be in the form of a non-conductive center core 403 that is covered by a conductive layer 402. For ease of reference, the conductive layer 402 over the non-conductive cente core 403 is referred to herein as the "inner conductive layer" in order to distinguish it from the transparent conducting oxide layer 203, which may be referred to as the "outer conductive layer." in this embodiment, the radius of the core (r_c) may be measured from the center of the non-conductive center 403 io the outer surface of the inner conductive layer 402.

1001001 In an embodiment, the inner conductive layer 402 ma be a metal or metal alloy; such as gold, copper, nickel, molybdenum, iron, aluminum, silver or alloys of the same, in an embodiment, the non-conductive center 403 may include a polymer, glass, a composite material, or a semiconductor material.

10101] The embodiment illustrated in FIGs. 4A, 4B, 4C, and 4D may exhibit energ conversion performance characteristics that are similar to embodiments featuring a solid conductive core when designed according to the embodiment methods described above, with the added benefit o f enabling the use of less-expensive or easier to process materials for the bristle cores. For example, this embodiment would enable productio of photovoltaic bristles with plastic or polymer cores, such as could be manufactured using stamping, pressing or molding techniques. While using such materials ma require adjustments in the diameter of the core in order to achieve desirable

manufacturing yields, the embodiment design methods described above enable the design of embodiment photovoltaic cells with similar performance characteristics.

[0102] FIGs. 5A, 5B, 5C, and 50 illustrate an embodiment photovoltaic cell 500 in which the absorption layer 207 in the photo voltaic bristles 20 la-20 Id include three absorber sublayers or regions 204. 302, 205, and non-conductive core centers 403

.5.) covered with an inner conductive layer 402 is described above. Thus, this embodiment is an example of a combination of the embodiments desc ribed above.

[0.103] FIGs. 6A, 6B, 6C, and 6D illustrate an embodiment photovoltaic cell. 600 in which the absorption layer .207 of photovoltaic bristles comprises a single layer and the core 206 comprises a semiconductor. In this embodiment, the semiconductor core 206 may be made from a p-type or n-type semiconductor material so that the junction of the absorption layer 207 and the semiconductor core 206 form a p-n junction suitable to convert photons into electro-hole pairs.

[01 4] in an embodiment, the semiconductor core 206 may be a p-type semiconductor material and the absorber sublayer 207 may be a n-type semiconductor material.

Alternatively, the semiconductor core 206 may be a n-type semiconductor material and the absorber sublayer 207 may be a p-type semiconductor material. In an embodiment, the semiconductor material for the core 206 and the absorber sublayer 207 may be different materials. For example, the semiconductor core 206 may be p-type cadmium telluride and the absorber sublayer 207 may be n-type cadmium sulfide. As another example, the semiconductor core 206 may be n-type cadmium sulfide and. the absorption layer 207 may be p-type cadmium telluride.

[0105] in another embodiment, the semiconductor materials for the semiconductor core 206 and the absorber sublayer 207 may be the same semiconductor materials. For example, the semiconductor core 206 may include a p-type amorphous silicon and the absorber sublayer 207 may include a n-type amorphous silicon. Alternatively, the semiconductor core 206 may include a n-type amorphous silicon and the absorber sublayer 207 may include a p-type amorphous silicon. The semiconductor core 206 may made from one or more of silicon, amorphous silicon, polycrystalline silicon, single crystal silicon, cadmium telluride, gallium arsenide, aluminum gallium arsenide, cadmium sulfide, copper indiu selenide, and copper indium gallium selenide. The absorber sublaye 207 may be made from one or more of silicon, amorphous silicon. polycrystalline silicon, single crystal silicon, cadmium telluride, gallium arsenide, aluminum gallium arsenide, cadmium sulfide, copper indium selenide, and copper indium gallium selenide,

[0106] FIGs. 7 A, 7B, 7C, and 7D illustrate an embodiment photovoltaic- cell 700 In which the core 206 of the photovoltaic bristles is made from a semiconductor, and the absorption layer 207 is made up of two absorber sublayers 204, 205, the inner layer of which combines with the semiconductor core 206 so that a p-i-n junction is formed. In an embodiment, the semiconductor core 206, the absorber sublayer 205, absorber sublayer 204 may be a p-type semiconductor material, an intrinsic semiconductor material and a n-type semiconductor material, respectively, in another embodiment, the semiconductor core 206, the absorber sublayer 205, and the absorber sublayer 204 may^¬ be a n-type semiconductor material, an intrinsic semiconductor material, and a p-type semiconductor material, respectively.

[010 1 In an embodiment, the semiconductor material for the core 206 and the absorber sublayers 204, 205 may be different materials. For example, the core 206, the absorber sublayers 205, 204 may include p-type cadmium telluride, intrinsic cadmium telluride, and n-type cadmium sulfide, respectively. In an alternative example, the core 206 and the absorber sublayers 205, 204 may include a n-type cadmium sulfide, intrinsic cadmium telluride, and a p-type cadmium telluride, respectively.

[0108] In an embodiment, the semiconductor materials for the semiconductor core 206 and the absorber sublayers 204, 205 may be the same semiconductor materials. For example, the semiconductor core 206, the absorber sublayers 205, 204 may include a p- type amorphous silicon, an intrinsic amorphous silicon, and a n-type amorphous silicon, respectively. In an alternative example, the semiconductor core 206 and the absorber sublayers 205, 204 may include a n-type amorphous silicon, an intrinsic amorphous silicon, and a p-type amorphous silicon. [0 J 09] The semiconductor core 206 may be made from one or more of silicon, amorphous silicon, poly crystalline silicon, single crystal silicon, cadmium telluride, gallium arsenide, cadmium sulfide, copper indium selenide, and copper indium gallium selenide. The absorber sublayers or regions 204, 205 may be made from one or more of silicon, amorphous silicon, polycrystalhne silicon, single crystal silicon, cadmium telluride, gallium arsenide, cadmium sulfide, copper indium selenide, and copper indium gallium selenide,

(0110] FIG. 8 illustrates an embodiment method 800 for manufacturing a photovoltaic cell made up of a array of photovoltaic bristles as described above, in block 802 a substrate may be formed. In an embodiment, the substrate may be formed by selecting a base material arid forming the substrate material to a desired shape. As discussed above the substrate may be glass, doped semiconductor, diamond, metal, a polymer, ceramics, or a variety of composite materials.

[0111 J In block 804 approximately cylindrical cores may be formed on the substrate. In an embodiment, cylindrical cores may be formed by a variety of processes. For example, metal cores may be grown up from the substrate through a mask using plating, vapor deposiiion and other similar well known processes. As another example, semiconductor cores may be grown up from die substrate using vapor deposition methods well known in the semiconductor processing parts. Plastic polymer cores may be made by molding or stamping cylindrical cores out of the substrate. In another embodiment, cylindrical cores may be formed by depositing a core layer over the substrate and stamping cylindrical cores out of the deposited core layer, In another embodiment, cylindrical cores may be formed by depositing a core layer over the substrate and etching cylindrical cores from the deposited core layer, in another embodiment, cylindrical cores may be formed by placing a template over the substrate and depositing material into the template, thereby forming cylindrical cores. The cores formed in the processes of block 804 may position and size the cores with dimensions and spacing determined using the design equations described above, [0112] in optional block 806 the cylindrical cores may be further processed, such as to increase the structural strength of the cylindrical cores formed in block 804. The operations of optional block 806 may be performed in embodiments in which the cylindrical cores are made of a non-conductive materials, such as a polymer. As an example, the cylindrical cores may be processes to form a rigid shape (e.g., a cylinder) b exposing them to elevated temperatures or electromagnetic radiation that leads to a hardening process. Processes that may be accomplished in optional block 806 may include processes that promote polymerization, cross-linking, or curing to make the material stronger or more rigid.

[0113] When the core material is nonconductive, in optional block 808 an inner conductive layer may be formed on the cylindrical cores, in this process, the conductive layer may be applied with the thickness sufficient to conduct the expected amount of current when the photovoltaic ceils are exposed to the design level of insolation. In an embodiment, the inner conductive layer may be formed by striking a conductive layer onto the cylindrical cores. In another embodiment, an inner conductive layer may be formed by depositing the inner conductive layer by any of chemical vapor deposition, plasma-enhanced chemical vapor deposition, atomic layer chemical vapor deposition, sputtering, plating, physical vapor deposition, ion plating, and coding with a wet- chemical process.

[011 ] In block 810 an absorption layer may be formed over the cylindrical cores. In an embodiment, the absorption layer may be formed by sequentially depositing a number of semiconductor sublayers over the core. For example, a p-type cadmium telluride sublaye may be applied followed by application an n-type cadmium sulfide sublayer, in an embodiment, the absorption layer may be deposited using well-known semiconductor processing techniques, such as by chemical vapor deposition, plasma-enhanced chemical vapor deposition, atomic layer chemical vapor deposition, physical vapor deposition, ion plating, sputtering, etc. As part of block 810, each of the applied semiconductor sublayers may be forther processed, such as to apply a desired level of dopant to generate the p-type or n-type semiconductor material in the region of the junction., and/or to adjust the index of refraction of the layer.

[0115 ) in block 812 an outer conductive layer ma be formed over the absorption layer, in an embodiment, the outer conductive layer may be deposited using well-known semiconductor and solar cell manufacturing raethods, such as by chemical vapor deposition, plasma-enhanced chemical vapor deposition, atomic layer chemical vapor deposition, physical vapor deposition, ion plating, sputtering, etc. As part of block 81.2, outer conductive layer may be further processed, such as to adjust the index of refraction of the layer.

[0116] In an. alternative method, the photovoltaic bristles may be created in the reverse direction with a non-solid core. Nanoprintmg techniques well known in the art may create an array of vias out of an optically transparent material (e.g., a transparent conductive oxide, a transparent conductive nitride, or an optically transparent polymer). Alternatively, vias could be formed by etching or ablation of a glass material. The absorption layer including any number of sublayers may be formed within the vias and as well as over the optically transparent material between the vias. The deposition raethods used to deposit the semiconductor layers into vias may be similar to those used in depositing semiconductor layers over the core (e.g., chemical vapor deposition). An inner conductive layer (i.e., a back conductor layer) may be formed within and between the vias over the last semiconductor layer. The inner conductive layer may be added by sputtering or evaporative techniques well known in the art. When the device is completed, the vias are rotated 1 80 degrees presenting the optically transparent layers outward. Thus, depending on the material thickness used for the back conductor layer, a void may remain in the vias resulting i a non-solid core,

[0117 j As mentioned above, in addition to increasing the percentage of photons absorbed and converted into electrical energy, the various embodiment photovoltaic bristle structures also exhibit unexpected improvements in electrical conductivity when exposed to light energy. This effect has been observed in prototypes, and may be due, at least in pari, to electric field effects in the transparent conductive layer caused by electric field concentrations at the points of discontinuities (e.g., sharp comers) in the structures. The photovoltaic bristle structure of the various embodiments features discontinuities in the outer conductive layer. These structural discontinuities occur at the base, (i.e., where the bristle couples to the substrate) and near the tip of each bristle. When the photovoltaic bristles are exposed to light the photovoltaic effect in the photovoltaic layer causes electrons and holes to move to the inner and outer conductive layers. Due to the surface shapes at the base and tip of the photovoltaic bristles, which form sharp comers, the electric charge on the surface may be greater in these locations than that exhibited in traditional planar photovoltaic cells. More important, the discontinuities near the connection of the bristle to the substrate and near the dp ma result in substantially higher electric fields in the transparent conductive layer in these regions. Testing of prototypes of embodiment photocel ls have detected surprisingly low resistance of the transparent conducting layer when the cell is exposed to light. This substantial reduction in electrical resistance in the transparent conducti ve layer may reduce the electrical losses due to resistance through the phoiovoltaic cell. Consequently, more electricity may be produced from an embodiment photovoltaic cell than would be expected considering the normal resistance of outer conductive layer materials.

(01.18) While the specific physics involved in reducing the electrical resistance of the outer conductive layer (e.g., a transparent conductive oxide) are not fully understood, testing of the prototy pes suggest that the effect may be related to the electric field concentrations in the structural discontinuities at the tip and base of the photovoltaic bristles. One possible explanation, although not intended to be a limitation on the claims, is that the electric field concentration in these regions of the photovoltaic bristles result in a change in the electrical resistance of the materials similar to what occurs in a field effect transistor when an electric field is applied. By significantly decreasing the electrical resistance in the regions of high electric field concentrations, the average electrical resistance through the outer conductive layer across an array of photovoltaic bristles may be substantially reduced. This effect is believed to be related to shapes and sizes of embodiment photovoltaic bristle structures, and thus unique to the structures of the various embodiments.

[0119| The electric field concentration effects are illustrated in FIG. 9. FIG. 9 illustrates an embodiment in which the semiconductor materials in the absorption sublayers 504, 506 are arranged such that electrons migrate to the outer conductive layer 203 and holes migrate to the conductive core 206. This is strictly for illustration purposes, because in other embodiments the polarity of the absorption sublayers 504, 506 may be reversed such that electrons migrate to the conductive core 206. As illustrated in FIG. 9, electrons and holes along the length of the photovoltaic bristles (i.e. in the regions 904 and 908) will flow through the inner and outer conductive layers 206, 203, resulting in an average field concentration that is a function of the rate of photon absorption.

Current flowing from these regions 904 and 908 to the conductors on the substrate 102 will encounter structural discontinuities where the bristle joins the substrate, which can lead to a concentration of charges 902, 906. Similar field concentrations may occu near the corners the tips of the photovoltaic bristles as illustrated. This concentration of charges at the tips and base of the photovoltaie bristles may result in an increased electric field between the concentrations electrons 902 on one conductive layer and of holes 906 on the opposite conductive layer. This local concentration electrons and holes may result in a locally enhanced electric field, which is believed to be at least part of cause the observed reduced electrical resistance in the outer conductive layer.

[0120] FIG. iOA-lOD illustrates the multiple embodiments for the outer conductive layer 203, FIG. 10A illustrates that the outer conductive layer 203 may comprise multiple layers as shown in the examples in FIGs. 10B- IOC. Although FIGs 10B- IOC only illustrate up to three sublayers within the outer conductive layer 203, any number of sublayers and combinations of materials for these sublayers are envisioned. For example, an outer conductive layer may include five sublayers with three thin conductive sublayers separated by two non-conductive sublayers. By including multiple sublayers, the outer conductive layer 203 may include a total thickness that achieves the proper optical depth (d_< .;) for enhanced transmissive properties in the design equations while also including a thin conductive sublayer providing the added field effect benefits described above.

Additionally; the multiple sublayers within the outer conductive layer 203 may add flexibility to each photovoltaic bristle 201.

[0121] To hel achieve an outer conductive layer 203 thick enough to exhibit high iransniissive properties while simultaneously thin enough to exhibit the field effect benefits within each photovoltaic bristle 201 , the outer conductive layer 203 may include two sublayers including a conductive sublayer 1012 (T ) and a non-conductive sublayer 1 14 (T C) as shown in F G. 10B. The conductive sublayer may be any suitable transparent conductive material with a thickness of approximately 500 to 15,000 angstroms. Some suitable transparent conductive materials may include, a transparent conductive oxide (e.g., indium tin oxide, zinc oxide, titanium oxide, etc), a transparent conductive nitride (e.g., titanium nitride), or a transparent conductive polymer.

Alternatively, the conductive sublayer 1012 may include a thin metal conductor such as gold or nickel to achieve high conductive field effect. The non-conductive sublayer 1014 may be any optically transparent material known in the art. such as a non-conductive optically transparent polymer, an optically transparent gel, or a dielectric layer, which makes up the difference between the thin conductive sublayer 1012 and the required thickness (d_i> i) for the entire outer conductive layer 203 , The non-conductive sublayer 1014 and the conductive sublayer 1012 may match the required index of^" refraction (n_(iCj) for the outer conductive layer 203. Instead of including a non-conductive sublayer 1014, the outer conductive layer 203 may include two different conductive sublayers 1012, 1016 as shown in FIG. IOC. For example, the outer conductive layer 203 may include a transparent conductive oxide such as titanium oxide (Ti0₂) and a transparent conductive nitride such titanium nitride (TIN). The two conductive sublayers 1012, 1016 may combine to achieve the required optical depth (d_oci) for the design formulas while individually being thin enough to exhibit the field effect benefits, hi an embodiment, the outer conductive layer 203 may include three sublayers such as a non-conductive sublayer 1014 separating two conductive sublayers 1012, 1016 as shown in FIG. 10D. The two conductive sublayers 1012, 1016 may each exhibit field effects leading the outer conductive layer 203 and the photovoltaic bristle 201 to have benefits from the multiple field effects. Additionally, the non-conductive sublayer 1014 combined with the two conductive sublayers 1012, 1016 may provide better iransmissive properties by achieving a desired total thickness in the outer conductive layer 203 as well as adding flexibility to the photovoltaic bristle 201 than only having a single thin conductive layer exhibiting Held effects.

[01 2] As described above, reductions in resistance of the transparent conductive layer due to electric field effects transparent conduction allows for the use of very thin transparent conductive layers in embodiment photovoltaic bristles. Prototype

embodiment photovoltaic ceils have been manufactured with transparent conductive layers with a thickness of 1500 angstroms. Based on analysis and such testing, it is believed that thinner transparent conductive layers may be achievable. Thinning the transparent conductive layers may enable the use of sma ller diameter cores and/or the addition of a transparent optical layer over the transparent conductive layer.

[0123] As mentioned abo ve, the wave interactions of photons with arrays of

photovoltaic bristles designed according to the embodiment design equations described above have been analyzed using classical electrodynamics and quantum mechanical models. These electrodynamic and quantum mechanical models take into account the wave interactions of photons with the regular and close spaced array of photovoltaic bristles, as well as the wave interactions with the transparent conducting oxide layer, and other layers in the design. These electrodynamic and quantum mechanical models also account for the internal refractio characteristics described above that are enabled by properly selecting the layer materials and thicknesses. These analyses reveal that a large fraction of the photons entering an embodiment array of photovoltaic bristles are absorbed into the bristles, where a large fraction of the incident photons are absorbed in the photovoltaic materials. These analysis results are illustrated in FIG. 11 which illustrate the probability of finding a photon at a given location in terms of brightness (i.e., dark regions are where there is a low probability that a photon exists). Specifically, FIG, 1 ! illustrates that photons striking an array of photovoltaic bristles are quickly absorbed into and largely remain trapped within the transparent conducting oxide and photovoltaic absorption layers.

§012 1 The preceding description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention, Tims, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the following claims and the principles and novel features disclosed herein.

Claims

What is claimed is:

L A photovoltaic cell, comprising:

an arra of photovoltaic bristles, wherein each photovoltaic bristle comprises: a core having a core radius (r_c):

an absorption layer positioned over the core and having a first radial thickness (d_ah,,); and

an outer conductive layer positioned over the absorption layer, having a second radial thickness (d _tj_. and an inde o f refraction (n_oe)),

wherein each bristle is configured such that:

namb * O^'er + abs + ^o l) wherein ii_(mf, is the the index of refraction of an ambient material surrounding the bristles.

2. The photovoltaic cell of claim 1, wherein the second radial thickness fd_oc;) is smaller than the first radial thickness (d»bs)-

3. The photovoltaic cell of claim 2, wherein the second radial thickness (d„;) is approximately two-thirds of the first radial thickness (d^ .

4. The photovoltaic ceil of claim ί , wherein the first radial thickness (c _s) is 50 microns or less.

5. The photovoltaic cell of claim 4, wherein the first radial thickness (d_ahs) is greater than or equal to 0.1 microns.

6. The photovoltaic cell of claim ! , wherein the absorption, layer comprises: a p-fype region; and

a ii-type region, and

wberein the entire absorption layer, including the p-type region and the n-type region, is fully depleted,

7. The photovoltaic cell of claim 1 , wherein the absorption layer comprises:

a p-type semiconductor sublayer over the core; and

an n-type semiconductor sublayer over the p-type semiconductor sublayer, and wberein the entire absorption layer, including the p-type semiconductor sublayer and the n-iype semiconductor sublayer_^ is fully depleted.

8. The photovoltaic cell of claim 1 , wherein the absorption layer comprises:

a n-type semiconductor sublayer over the core; and

a p-type semiconductor sublayer over the n-type semiconductor sublayer, and wherein the entire absorption layer, including the n-type semiconductor sublayer and the p-type semiconductor sublayer, is fully depleted,

9. The photovoltaic cell of claim 1 , wherein an absorption layer index of refraction is greater than the outer conductive layer index of refraction (n^).

10. The photovoltaic cell of claim 1, wherein a height of the photovoltaic bristle is greater than or equal t 1 microns.

1 1 . The photovoltaic cell of claim 10, wherein the height of the photovoltaic bristle is less than or equal to 100 microns.

12. The photovoltaic bristle of claim I , wherein the absorption lay er is made from semiconductor material selec ted from the group of silicon, amorphous silicon. poIycrystaHine silicon, single crystal silicon, cadmium teikiride, gallium arsenide, aluminum gallium arsenide, cadmium sulfide, copper indium selenide, and copper indium gallium selenide,

13. The photovoltaic bristle of claim 1 , wherein the outer conductive layer is made from one or more of zinc oxide , indium tin oxide, cadmium tin oxide, and titanium oxide.

14. The photovoltaic bristle of claim 1 , wherein the outer conductive layer comprises a transparent conductive nitride.

15. The photovoltaic bristle of claim 1 , wherein the outer conductive layer comprises multi le sublay ers .

16. The photovoltaic bristle of claim 15, wherein the outer conductive layer comprises a conductive sublayer and a non-conductive subkver.

17. The photovoltaic bristle of claim 15, wherein the outer conductive layer comprises two different conductive sublayers.

18. The photovoltaic bristle of claim 1, wherein the core is a metallic core.

19. The photovoltaic bristle of claim 18, wherein the core is made from one o more of gold, copper, nickel, molybdenum, iron, aluminum, and silver,

20. The photovoltaic bristle of claim 1 , wherein the core comprises:

an inner core made from a non-conductive material; and

a conductive layer surrounding the inner core.

21. The pliotovoiiaic bristle of claim 1, wherein the core comprises one or more of silicon, amorphous silicon, polycrystalline silicon, single crystal silicon, cadmium tellurite, gallium arsenide, gallium aluminum arsenide, cadmium sulfide, copper indium seiemde. and copper indium gallium selenide.

22. The photovoltaic bristle of claim 1, wherein the core is a non-solid core.

23. The photovoltaic bristle of claim 1 , wherein a height (I of the photovoltaic bristles satisfies the equation:

(((X.67*<t_fl6s)+r_r (2 (0.9))

24. The photovoltaic bristle of claim 1 , wherein the array of photovoltaic bristles are arranged such that an edge to edge spacing between neighboring photovoltaic bristles (¾_ΟΕ) satisfies the equation:

((1.67 * d_abs) + r_c) * (2) * (0.9) < P_EtoE≤ ((1.67 * d_abs) + r_c) * (2) * (1.1).

25. The photovoltaic bristle of claim 23 , wherein the array of photo voltaic bristles are arranged such that an edge to edge spacing between neighboring photovoltaic bristles (P_HOE) satisfies the equation:

((1.67 * d_a ) 4- r_c) * (2) * (0.9) < P_stoB < ((1.67 * d_abs + r_c) * (2) * (1.1).

26. The photovoltaic cell of claim 1 wherein the array of photovoltaic bristles defines a. surface configured so that light energy conversion efficiency of the photovoltaic cell is greater when incident light strikes the surface at an angle less than ninet degrees than when incident light strikes the surface at an angle of approximately ninety degrees.

27. A method of generating electricity, comprising: exposing a photovoltaic cell comprising an array of photovoltaic bristles to light, wherein each photovoltaic bristle comprises:

a core having a core radius (r_e);

an absorption layer positioned over the core and having a first radial thickness

an outer conductive layer positioned over the absorption layer, having a second radial thickness (d_oci), and an index of refraction (n_»Ci)_?

wherein eac photovoltaic bristle is configured such that; wherein / _> i the the index of refraction of an ambient material surrounding the bristles.

28. A method of manufacturing -a photovoltaic cell, comprising:

forming a substrate; and

forming an array of photovoltaic bristles extending from the substrate, wherei forming the array of photovoltaic bristles comprises:

forming on the substrate an array of cores having a core radius (r_c); depositing an absorption layer over the arra of cores to a first radial thickness (d.^); and

depositing an outer conductive layer over the absorption layer to a second radial thickness (d^), wherein the outer conductive layer has an index of refraction (n.,_c:h

wherein each photovoltaic bristle in the array is configured such that:

n-amb * c + dabs + doci) wherein ¾,„/, is the the index of refraction of an ambient material surrounding the bristles.

29, The method of manufacturing of claim 28, wherein forming an array of photovoltaic bristles extending from the substrate comprises forming the array of photovoltaic bristles such that a edge-to-edge spacing between neighboring photovoltaic bristles

satisfies the equation:

((1.67 * d_abs) + r_c) * (2) * (0,9) < P_BteE < ((1.67 * d_abs) + r_c) * (2) * (1.1).

30, The method of claim 28, wherein forming an array of photovoltaic bristles extending from the substrate comprises forming the array of photovoltaic bristles such that the photovoltaic bristles have an average minimum height (h_mm) that satisfies the equation;

31. The method of claim 28, wherein depositing the absorption layer over the array of cores to a first radial ihickness (d_{a s}) and depositing the outer conductive layer over the absorption layer to the second radial thickness (d^i) are accomplished so that the second radial thickness (d_ocs) is smaller than the first radial thickness (d_a¾s).

32. The method of claim 28, wherein depositing the absorption laye over the array of cores comprises:

depositing a fully depleted p~type semiconductor sublayer over the core; and depositing a fully depleted n-type semiconductor sublayer over the p-type semiconductor sublayer.

33. The method of claim 28, wherein depositing the absorption layer over the array of cores comprises:

depositing a fully depleted n-type semiconductor sublayer over the core; and depositing a full depleted p-type semiconductor sublayer over an n-type semiconductor sublayer.

34, The method of claim 28, wherein the absorption layer has an index of refraction ί ¾„) that is greater than the outer conductive layer index of refraction (n_0¾i).

35, The method of claim 28, wherein depositing the absorption layer over the array of cores comprises depositing a layer comprising one or more of silicon, amorphous silicon, polycrystalline silicon, single crystal silicon, cadmium teiluride, gallium arsenide, aluminum gailium arsenide, cadmium sulfide, copper indium selenicie, and copper indium gallium selentde.

36, The method of claim 28, wherein depositing the outer conductive layer over the absorption layer comprises depositing a layer comprising one or more of zinc oxide, indium tin oxide, cadmium tin oxide, and titanium oxide,

37, The method of claim 28, wherein depositing the outer conductive layer over the absorption layer comprises depositing a layer comprising a transparent conductive nitride.

38, The method of claim 28, wherein depositing the outer conducive layer includes depositing multiple sublayers.

39, The method of claim 38 , wherein depositing multiple sublayers comprises a

conductive sublayer and a non-conductive sublayer,

40, The method of claim 38 , wherein depositing multiple layers comprises two different conductive sublayers.

41, The method of c laim 28 , wherei n forming on the substrate an array of cores comprises forming on the substrate an array of metallic cores.

42, The method of claim 28, wherein forming on the substrate an arrav of cores comprises:

forming on the substrate an array of metallic cores and

depositi ng a conductive layer over the array of metalli c cores.

43. The method of claim 42, wherein depositing a conductive layer over the array of metallic cores comprises deposing over the array of metallic cores a lay er of one or mor of gold, copper, nickel, molybdenum, iron, aluminum, and silver.

44. The method of claim 28, wherein forming on the substrate an array of cores comprises forming on the substrate an array of semiconductor cores comprising one or more of silicon, amorphous silicon, polycrystalHne silicon, single crystal silicon, cadmium telluride, gallium arsenide, gallium aluminum arsenide, cadmium sulfide, copper indium selenide, and copper indium gallium selenitic.

45, A method of manufacturing a photovoltaic cell, comprising:

forming an array of photovoltaic bristles, wherein forming the arra of photovoltaic bristles comprises:

forming an array of vias out of an outer conductive layer with a second radial thickness of (d_OC(), wherein the outer conductive layer has an index of refraction of

depositing an absorption layer withi and between each via to a first radial thickness (d_at)S);

depositing a core over the absorption layer to a core radius

wherein each bristle in the array of photovoltaic bristles is configured such that:

no l * ^rc ^

>½,·».» * (r_c 4- d_Qbs + ⁽tod) ~ wherein n_m)f, is the the index of refraction of an. ambient, material surrounding the bristles.

46, The method of manufacturing of claim 45, wherein depositing the core comprises depositing a non-solid core and a core radius (r_e) comprising a void.